On Nonlinear Abstract Neutral Differential Equations with Deviated Argument

Existence of solutions to neutral differential equations with deviated argument

In this paper we shall study a neutral differential equation with deviated argument in an arbitrary Banach space X. With the help of the analytic semigroups theory and fixed point method we establish the existence and uniqueness of solutions of the given problem. Finally, we give examples to illustrate the applications of the abstract results.

Almost Automorphic Mild Solutions to Some Semilinear Abstract Differential Equations with Deviated Argument in Fréchet Spaces

In this paper we consider the semilinear differential equation with deviated argument in a Fréchet space x(t) = Ax(t) + f(t, x(t), x[α(x(t), t)]), t ∈ R, where A is the infinitesimal (bounded) generator of a C0-semigroup satisfying some conditions of exponential stability. Under suitable conditions on the functions f and α we prove the existence and uniqueness of an almost automorphic mild solu...

Stability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY

Differential transformation method for solving a neutral functional-differential equation with proportional delays

In this article differential transformation method (DTMs) has been used to solve neutral functional-differential equations with proportional delays. The method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. Exact solutions can also be obtained from the kno...